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I have the exact same setup on one of my machines. The first time I encountered this problem, I fought it for hours. It's really a very simple problem, but when you're a Linux newbie, it seems like a mountain. You just don't have your gateway address in the configuration. Go back through the network configuration procedure, and make sure you got it all. If it still doesn't work, I can get you some file names where you can set it manually. That's what I had to do. The only hard part is finding the files.

Hey ChipPunk RedHat 7.0 lets you install the network configuration when you do an install, so if you really can't find the settings or files... re-install, however this is a stupid solution to your problem.

to solve your prob: make sure all connections and your NIC are working, then make sure your IP settings and default gateway are correct.
to do that, do the following: log in
got to an Xterm, get root access by typing su - after you've done that, enter your root password. Type Linuxconf enter the network tab in linuxconf, enter your IP adress, perhaps your linksys can do DHCP? If it does, leave your IP adress blank and set IP settings to auto recieve (DHCP) ; otherwise manual: enter your IP (something like 192.168.1.11 and submask 255.255.255.0) now you have to enter the default gateway and DNS. Ok. press accept and quit Linuxconf.

Now your back in your Xterm. Enter the following commands (assuming you have your NIC at eth0 and you have chosen 192.168.1.11 as IP adress for your box and 192.168.1.10 four your Gateway box)

ifconfig eth0 192.168.1.11 netmask 255.255.255.0 up

route add -net 192.1.ethernetmask 255.255.255.0 eth0

route add default gw 192.168.1.10 eth0

exit

exit

now your connection should be working fine
however don't shoot me if I accidentally typed some mistake here...

Stflook is exactly right....I would just like to give an explanation why.

Your router obviously has 2 physical interfaces. One interface sits on your internal network and the other is on the network that connects to your ISP. Now since you are the same network segment as the internal interface of the router, you will be able to ping the router no problem. Any traffic that is destined for another network other than your own (in this case the Internet) does not know where to go, and if you do a ping you will get "destination host unreachable". By setting the default gateway on your machine, you are telling your machine that for any IP address that is not on it's same network, send it to a router to route the traffic (the default gateway)

Another way to test this and verify that it is not your Internet connection itself, is to ping the IP address of the external interface on your router, if you get the same response, it is because the traffic does not know where to go (or it is a bad router, which is not likely )

I know for some of you guys this might be easy, but for any noobs that have ever wondered what exactly the default gateway setting is for, now you know!!